Cloth simulation - simulate 2 unlinked meshes together as one
Let's assume the stitches or other details can be represented by some cubes close to the flag geometry.



Duplicate the Flag mesh. The FlagDupe should also do the same simulation as the original. We will create a cage from it for the extras.

Add a displace modifier, and a solidify modifier. The value of the second modifier should be twice the value of the first modifier.



Select the stitched extra object, add a MeshCage Modifier to them and bind the object to the FlagDupe by clicking on the bind button.



The bound object will follow the FlageDupe object.